APPROXIMATE METHOD TO SOLVE PROBLEMS OF HEAT AND MASS TRANSFER UNDER WATER FREEZING IN PERMAFROST ROCKS

The problems of predicting heat and humidity conditions in various mine structures, as well as taking into account induced pollution of frozen soil and pollutant migration in permafrost strata need new mathematical models. It is required that these models take into account to a fuller extent features of physical freezing and thawing processes in pore water. It is also of the current concern to develop new software tools and methods for the numerical solution of model problems on heat–moisture–salt transfer in multi-dimensional domains with regard to phase ice–solution transition. This article proposes a method to solve the problems of heat and and mass transfer with phase transformation (freezing–thawing). The method involves splitting of the initial problem of heat and mass transfer with phase transformation with respect to physical processes. Such processes are assumed to be diffusion transfer of heat, moisture and soluble salt between points of meshing, as well as the processes of redistribution in the point neighborhoods which are assumed to be isolated systems. The developed algorithm allows calculating complex processes including phase transformations while integrating solutions of nonlinear equations of thermal conduction in application packages. Irrespective of space parameters (at the stage of phase transformations), the algorithm makes it possible to use equations of phase equilibrium both for the processes with narrow and wide temperature range of the phase transfer zone (Stefan problem type), including multi-front and multidimensional processes, in the framework of the common methodical approach. Tests of the similarity and numerical solutions show a satisfactory agreement (accurate to 2%). This offers good prospects for further applications.

Keywords

Heat and mass transfer, phase transformations, splitting with respect to physical processes, solution method.

Issue number: 12
Year: 2018
ISBN:
UDK: 622.45:536.421
DOI: 10.25018/0236-1493-2018-12-0-57-64
Authors: Popov V. I., Kurilko A. S.

About authors: Popov V.I., Candidate of Technical Sciences, Senior Researcher, e-mail: popov.gtf@mail.ru, Kurilko A.S., Doctor of Technical Sciences, Professor, Deputy Director for Science, Chersky Mining Institute of the North, Siberian Branch, Russian Academy of Sciences, 677000, Yakutsk, Russia.

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